You may be confusing bits and bytes. Many EPROM programmers and programmer software will display a bunch of bytes in the vicinity of the requested address. The display is almost always in hexadecimal digits. There are two hexadecimal digits in a byte. I have seldom, if ever, seen a programmer that displayed things in binary. Get a grip and read the manual. See if that helps to resolve things.

EPROMS like the 27C256 are organized as an array of bytes. So 32K bytes by 8 bits per byte. EPROMS that are organized in this way have no concept of how some processor might decide to put together a word. Little-Endian processors put the LSB at the lowest address. Big-Endian processors put the MSB at the lowes address.

In a system that wants to fetch a word at a time there might be two 27C256 EPROMS side by side. One would have the bytes at even addresses and one would have the bytes at odd addresses. If there was only a single EPROM the processor would have to fetch a word instruction by running two bus cycles back to back.